{"state_type":"pith_open_graph_state","state_version":"1.0","pith_number":"pith:2014:RRYPJVMKWLYIGOF757TXFAVZAE","merge_version":"pith-open-graph-merge-v1","event_count":2,"valid_event_count":2,"invalid_event_count":0,"equivocation_count":0,"current":{"canonical_record":{"metadata":{"abstract_canon_sha256":"73de615affc76402fcdc938f561d76175bca73430a8b544b8dccf14762f87e43","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-08T03:14:47Z","title_canon_sha256":"889e02625975306a60d02ba8b2ab28644f79f8e56e0314fc2557dbe73ed4ab05"},"schema_version":"1.0","source":{"id":"1409.2196","kind":"arxiv","version":1}},"source_aliases":[{"alias_kind":"arxiv","alias_value":"1409.2196","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"arxiv_version","alias_value":"1409.2196v1","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1409.2196","created_at":"2026-05-18T02:43:17Z"},{"alias_kind":"pith_short_12","alias_value":"RRYPJVMKWLYI","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_16","alias_value":"RRYPJVMKWLYIGOF7","created_at":"2026-05-18T12:28:46Z"},{"alias_kind":"pith_short_8","alias_value":"RRYPJVMK","created_at":"2026-05-18T12:28:46Z"}],"graph_snapshots":[{"event_id":"sha256:2b852a90752644c0c511153b7b6aeab917e5fe195dbbcc9c1be0b14f313083e3","target":"graph","created_at":"2026-05-18T02:43:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"graph_snapshot":{"author_claims":{"count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","strong_count":0},"builder_version":"pith-number-builder-2026-05-17-v1","claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"paper":{"abstract_excerpt":"The sectional curvature of the volume preserving diffeomorphism group of a Riemannian manifold $M$ can give information about the stability of inviscid, incompressible fluid flows on $M$. We demonstrate that the submanifold of the volumorphism group of the solid flat torus generated by axisymmetric fluid flows with swirl, denoted by $\\mathcal{D}_{\\mu,E}(M)$, has positive sectional curvature in every section containing the field $X = u(r)\\partial_\\theta$ iff $\\partial_r(ru^2)>0$. This is in sharp contrast to the situation on $\\mathcal{D}_{\\mu}(M)$, where only Killing fields $X$ have nonnegative","authors_text":"Pearce Washabaugh, Stephen C. Preston","cross_cats":[],"headline":"","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-08T03:14:47Z","title":"The Geometry of Axisymmetric Ideal Fluid Flows with Swirl"},"references":{"count":0,"internal_anchors":0,"resolved_work":0,"sample":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1409.2196","kind":"arxiv","version":1},"verdict":{"created_at":null,"id":null,"model_set":{},"one_line_summary":"","pipeline_version":null,"pith_extraction_headline":"","strongest_claim":"","weakest_assumption":""}},"verdict_id":null}}],"author_attestations":[],"timestamp_anchors":[],"storage_attestations":[],"citation_signatures":[],"replication_records":[],"corrections":[],"mirror_hints":[],"record_created":{"event_id":"sha256:962d044bd51454b932fb1bbdd441c192a7d50af610165da24c8f38a13b5d657d","target":"record","created_at":"2026-05-18T02:43:17Z","signer":{"key_id":"pith-v1-2026-05","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","signer_id":"pith.science","signer_type":"pith_registry"},"payload":{"attestation_state":"computed","canonical_record":{"metadata":{"abstract_canon_sha256":"73de615affc76402fcdc938f561d76175bca73430a8b544b8dccf14762f87e43","cross_cats_sorted":[],"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DG","submitted_at":"2014-09-08T03:14:47Z","title_canon_sha256":"889e02625975306a60d02ba8b2ab28644f79f8e56e0314fc2557dbe73ed4ab05"},"schema_version":"1.0","source":{"id":"1409.2196","kind":"arxiv","version":1}},"canonical_sha256":"8c70f4d58ab2f08338bfefe77282b90138ee66c2fb90fe6c827e8fe8ccaf40ae","receipt":{"algorithm":"ed25519","builder_version":"pith-number-builder-2026-05-17-v1","canonical_sha256":"8c70f4d58ab2f08338bfefe77282b90138ee66c2fb90fe6c827e8fe8ccaf40ae","first_computed_at":"2026-05-18T02:43:17.639124Z","key_id":"pith-v1-2026-05","kind":"pith_receipt","last_reissued_at":"2026-05-18T02:43:17.639124Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54","receipt_version":"0.3","signature_b64":"O46O6RoMTLPdRFmqMwKJr4CLhm/YPBO7vXAwprR8IAAlFHb/iF/eTXQH5RkAg5I2s0AAXNIyvUal7KcTiu/4Bw==","signature_status":"signed_v1","signed_at":"2026-05-18T02:43:17.639692Z","signed_message":"canonical_sha256_bytes"},"source_id":"1409.2196","source_kind":"arxiv","source_version":1}}},"equivocations":[],"invalid_events":[],"applied_event_ids":["sha256:962d044bd51454b932fb1bbdd441c192a7d50af610165da24c8f38a13b5d657d","sha256:2b852a90752644c0c511153b7b6aeab917e5fe195dbbcc9c1be0b14f313083e3"],"state_sha256":"06877f013da2d424aa703f516cf7f9d801c8902fb093d255c3c0167a21f6e72d"}